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ADJUSTMENTS 

OF 

ENGINEERING INSTRUMENTS 

AND 

HELD PROBLEMS 

IN 

SURVEYING 





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Book._ 






COPYRIGHT DEPOSIT. 



ADJUSTMENTS 

OF 

ENGINEERING INSTRUMENTS 
FIELD PROBLEMS 

IN 

SURVEYING 



S E coxd *: ditiox 

[Revised and Corrected 



coPYRir.n t ]•: i), 1905 

B V 

EDWARD N. PROUTY, B. S. 

Assoc. M. Am. Soc, C. E; Assistant Professor L\ L\ En&ineei ii • 
University of California 



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Twe Gopms tiecareu 

SEP M 1905 



PRESS OF fr? 



DAILY GAZETTE 



PREFACE 

The difficulties experienced during several years of in- 
structing engineering students in the rudiments of field 
surveying have led the author to issue this little book for 
a guide to the beginner and an assistance to the instructor. 

For the best instruction in field surveying, the work of 
the embryo surveyor needs almost constant supervision by 
the instructor. This is impossible where classes are large 
and the instructing force is small. 

Part I was written several years ago by Mr. Harry H. 
Hirst, then instructor in Civil Engineering at California, 
and was issued in pamphlet form by the department of 
Civil Engineering. This has here been revised and cor- 
rected. The object was to give an outline of those methods 
of making the adjustments of the common field instruments 
considered the best in accomplishing the desired end. Con- 
fusion of the student is thus avoided and when he has 
mastered a given instrument and obtained a clear idea of 
the object of each adjustment and the necessity for it, he 
may then refer to other methods of accomplishing the same 
results. 

That problem book is the best aid to the instructor in the 
field which is so definite in its direction to the student that 
he will need to reason why as little as possible and bend 
his energies to familiarizing his hands and eyes to how the 
end is accomplished. 

The discussion of the theory of surveying belongs to 
text-books and the class-room. When once the student has 
had the theory explained to him and then familiarizes 
himself with an approved method and obtains results 
thereby, he is in a position to see why there was a method 
and perhaps see also that there may be other methods of 
proceedure to accomplish similar results. 

Part II has been prepared as such an aid for the field 
instruction in the University of California. The forms 
of notes given with the problems are such that anyone at 
all conversant with the subject cannot fail to understand 
what they signify. Some of these forms are conventional 
with practicing surveyors. 

Little claim is made to originality by the writer; he has 
simply chosen what he considers the simplest, most prac- 
tical and efficient methods of accomplishing the end sought. 

Berkeley, August L, 1904. EDW. X. PROUTY. 



GENERAL REMARKS AND CAUTIONS. 



1. Remember that an engineering field instrument is an 
instrument of precision, and that to insure accurate results 
and reasonably perfect adjustment, care must be used in 
handling the instrument. 

2. Never rest the hands upon the legs of an instrument. 
It will surely be displaced if you do. 

3. Be sure that the thumb-nuts that fasten the tripod 
legs to the tripod-head are well tightened before beginning 
to level the instrument. In case these nuts bind, when the 
instrument is picked up and the legs closed, loosen them, 
re-tighten at the next set-up. 

4. If, in leveling an instrument, the leveling screws in 
one pair begin to bind, release one of the screws in the ad- 
jacent pair. 

5. Be sure that the leveling screws have a firm bearing 
on the tripod-head plate, without severe strain or binding. 

6. Always carry a level or a transit with the main 
motion (around the main axis) undamped. 

7. In leveling work, the level should never be clamped 
(except in making the adjustment). 

8. In adjustment of the eye-piece or cross-wires, always 
loosen both sets of capstan-headed screws before attempt- 
ing to move the reticule. NEVER FORCE ANY ADJUST- 
ING SCREW. 

9. The needle should never be undamped until the in- 
strument is set up and leveled. Always clamp the needle 
before moving the instrument. 



TO THE STUDENT 



1. Ascertain beforehand, if possible, what problem is 
assigned for the day, and read it over so there need be no 
delay in getting to work after receiving your equipment. 

2. Ordinary ground is seldom so firm that considerable 
moving about the instrument will not affect more or less 
the setting of the instrument. Hence it is advisable to 
stand in one position only while taking all the readings you 
can at any setting. For instance, while using the level, 
stand at about 45° from the line of the telescope when it is 
pointed to the rod. Standing thus, without either stepping 
or throwing the weight of the body from one foot to the 
other, you can easily bend slightly, one way to the eyepiece 
and the other way to read the bubble, and be at the same 
time in the position to give the most intelligible signals to 
your rodman. For you should 

3. Always give such signals to your rodman that their 
meaning can never be misunderstood. And Never give a 
signal to the rodman that a setting is good or that a read- 
ing has been taken until you have, immediately after mak- 
ing the setting or taken the reading, looked at the bubble 
and seen that it is well centered. If it is not, correct it, 
take a new reading and again read the bubble. 

4. When going through a doorway or narrow passage- 
way with an instrument, always carry it in front of you 
where you can see that nothing touches it. Never carry a 
line-rod or level-rod together with an instrument. 

5. Take all notes in as neat a manner as possible, print- 
ing them as indicated on the accompanying scale, for the 
notes taken at the time of observation are the ones to be 
handed in. No copying of notes will be tolerated, except 
where it is impossible to avod it. Calculations should be 
made at the time of observation in the case of level work 
as in problems V and VI, and as soon after the completion 
of the field work as possible in other cases. 

6. Your notes are the record of the work done when 
you are head chain-man or instrument-man. Whether you 
have done the recording yourself or the rodman has done 
it for you, you are responsible tor the results and should 
sign them and hand them in. 



PART I. 

ADJUSTMENT OF ENGINEERING AND FIELD INSTRU- 
MENTS. 

Before beginning the adjustment of any engineering in- 
strument, in which a telescopic line of sight is used, it is 
necessary, first of all, to so focus the eye-piece that ail 
parallactic effect may be eliminated. This is frequently 
called the adjustment for elimination of parallax, but is not 
strictly an adjustment. The elimination is accomplished as 
follows: Direct the telescope towards the sky. By means 
of the torsional motion which can be given to the eye-piece 
bring the cross-wires well into focus, the wires then appear- 
ing as deep black lines across the field of view. (In some 
instruments the eye-piece motion is obtained by means of 
a rack and pinion connected with a turn-screw on the side 
of the telescope). It will be found that as the eye-piece 
is moved in and out that the wires first appear very dimly, 
or not all, then gradually grow darker and darker, until 
a point of maximum blackness and opaqueness occurs, after 
which they will again gradually disappear. The wires are 
accurately in focus at the point of maximum blackness. 
Having set the eye-piece at this point, test the total elim- 
ination of parallax as follows : Direct the telescope towards 
some fixed object, and carefully focus the objective until 
the image is clear. Move the alidade and telescope until 
the intersection of the cross-wires covers some definite 
point on the object. If now the head of the observer (while 
looking through the telescope) be nodded gently back and 
forth, 'and the cress-wires appear to remain fixed on this 
point, all parallax is eliminated. If there is an apparent 
movement of the wires over the fixed point, some parallax 
remains and the adjustment must be repeated until the 
proper elimination is obtained. 

In adjusting any engineering instrument, it is almost 
impossible to make one adjustment without disturbing 
some other one. This is especially true when the instru- 
ment is badly out of adjustment. In the latter case it is 
well, therefore, to go over all the adjustments somewhat 
roughly at first, and then repeat them with as much ac- 
curacy as possible It is very seldom that in going over 
the adjustments the first time that accurate results are 



obtained. The adjustments should be retested and repeated 
until they are complete. 

A.— THE ENGINEER'S LEVEL. 

The essential adjustments of the engineer's level are 
three in number, viz.: 

1. The Collimation Adjustment. 

2. The Bubble Adjustment: Peg Method. 

3. The Y Adjustment. 

The field methods used in making these adjustments will 
now be described. 

1. The Collimation Adjustment. — Set the instrument up 
firmly, unfasten and throw back the clips which hold the 
telescope in the Y's. By means of the leveling-screws and 
the horizontal motion of the telescope around the instru- 
mental axis, using the clamp and tangent-screw, bring the 
intersection of the cross-wires to cover accurately a minute 
distant point. Carefully revolve the telescope in the Y's 
about its longitudinal axis, until it has been turned half- 
way around. Note whether the intersection of the cross- 
wires still covers the point. If not, move the reticule by 
means of the capstan-headed screws until the error is one- 
half corrected,, correcting first one wire and then the other. 
Reset the intersection on the fixed point by means of the 
leveling-screws and tangent-screw, and carefully revolve 
the telescope in the Y's to its original position. If the 
adjustment is correct the intersection of the cross-wires 
will still cover the point. If this is not true, repeat the 
adjustment until correct. 

The intersection of the wires having been thus brought 
into the telescopic axis, it is also necessary that the hori- 
zontal wire should be perpendicular to the instrumental 
axis. If this is true, the upright wire will be vertical when 
the instrument is leveled. To accomplish this, refasten 
the telescope in the clips, and place the horizontal win 
that one end of it (at the side of the field of view) shall 
cover a fixed point. Turn the telescope about the instru- 
mental axis and see if the point, in its apparent motion 
across the hold, follows the horizontal wire. If not. turn 
the reticule (being careful not to displace the centering of 
the intersection of the cross-wires) until the point will 



move along the horizontal wire, when the telescope is thus 
revolved around the main axis. The adjustment is then 
complete. 

2. The Bubble Adjustment: Peg Method. — In the pre- 
ceding adjustment we have placed the line of collimation in 
the axis of the telescope tube. The object of this second 
adjustment is to make the axis of the bubble-tube parallel 
to the line of collimation. When this adjustment has been 
made, the line of collimation will be truly horizontal when- 
ever the bubble is brought accurately to the center of the 
bubble-tube. There are several methods of accomplishing 
this result, but, in order to prevent confusion, only one 
method will be outlined here. The "peg" method, as it is 
called, is preferred by the large majority of engineers, and 
is, as can be shown, the most reliable means of making 
the bubble adjustment. Proceed as follows: On ground 
that is approximately level drive firmly two stakes at a 
distance apart equal to about 300 feet (d in figure 1). This 
distance may be paced. Set the level up midway between 
the stakes and in the same horizontal line. Read the rod 
held on each of the stakes A and B (figure 1) to thou- 
sandths, always having the bubble in the center of the 
bubble-tube whenever a reading is taken. Since A and B 
are equally distant from the instrument, all errors due to 
maladjustment as well as effects of curvature of the earth 
and refraction are eliminated in subtracting the rod read- 
ings to determine the difference of elevation between A 
and 'B. Hence the difference of rod readings on A and B 
Will be the true difference in elevation of A and B. Now 
set the level up at a point D in line with A and B and at 




a distance BD equal to one-tenth AB. (Any proportion 

8 



would do, of course, but one-tenth is a convenient ratio to 
use, as will appear). Level the instrument carefully and 
read the rod held on B. Provided there were no curvature 
of the earth or refraction to consider, the difference in 
elevation of A and B added (if B is higher than A) or sub- 
tracted (if B is lower than A) would give the rod reading 
on A, when the line of collimation is parallel to the axis of 
the bubble tube. For perfect work, however, a positive 
correction must be made for the combined effect of curva- 
ture and refraction. 

Let the reading on B, with level at D, be b; let the true 
difference between A and B be h (as determined with level 
at C) ; let the correction for curvature and refraction be c. 
Then if the instrument is in adjustment the reading on A 
will equal (b±h+c). h will be positive if B is higher than 
A; negative if B is lower than A. Let the reading on A 
(level at D) be a. Then a — (b±h+c) will be the error, due 
to maladjustment in the distance AB. We must correct, 
however,, for the distance AD which is 11-10 of AB, with 
the proportions as chosen. Hence the correction is 



<= : ^{j 



(b±h+c)| 



The correction for curvature and refraction, c, is 0.576 
feet in a mile and varies as the square of the distance. 
This gives the correction for a 200-foot sight as -J-0.001 and 
for a 300-foot sight as +0.002. 

After the true target-setting has been found and the 
target set, bring the horizontal cross-wire to cover the 
horizontal center line on the target, and then- adjust the 
bubble to the center of the tube by means of the screws at 
the end of the bubble-tube. After this adjustment is made 
a new rod reading is made on B, and the difference between 
the target setting on A and this new reading should be the 
same as the true difference. Any variation in this result 
gives the amount of error due to maladjustment still re- 
maining, and should not be greater than 0.003. 

While this adjustment may seem long from this descrip- 
tion of it, it will be found in the field to be much simpler 
i ban is apparent. If the notes are taken and kept in the 
following form, the simplicity of the operation will be 

shown at once. 



Example: — Peg Adjustment of B. & B. Level, No. 804. 



Instrument at C. 

Rod on A 4.381 

Rod on B 1.908 

True Difference. 2.473 



2. Instrument at D. 

Rod on B 3.407 

Correction of Curvature: 

DA = 300' -f 0.002 

True Difference 2.473 

Sum 5.882 

Rod reading on A 5.993 

Difference 0.111 

Difference x ^ 0.122 

Target Setting 5.871 

New Reading on B 3.397 

Curvature Correction +0.002 

Difference .' 2.472 

True Difference 2.473 

Error in Adjustment. . . .0.001 

Since "c" is not large it is very usual to omit it in mak- 
ing this adjustment. 

3. The Y Adjustment. — Adjustments 1 and 2 are neces- 
sary for accurate work. This adjustment is one of conve- 
nience, and its object is to make the axis of the bubble- 
tube perpendicular to the vertical axis of the instrument. 
If then the telescope be leveled in one position it will re- 
main level when revolved around the vertical axis of the 
instrument. The test and adjustment are made as follows: 
Set up and carefully level the instrument over both pairs 
of leveling screws. Bring the bubble to the center of its 
tube with the telescope over one pair of leveling screws. 
Revolve the instrument on its vertical axis 180°. If the 
bubble still remains in the center the Y adjustment is per- 
fect. If not, correct one-half the error by means of the 
leveling screws and the remaining half by means of the 
large capstan-nuts that hold the Y's to the horizontal bar. 
Revolve the instrument through 180° again and see if the 
bubble now remains in the center of its tube. If not, repeat 
the adjustment until perfect. 

B.— THE DUMPY LEVEL. 

In the dumpy level, there is no provision made for the Y 
adjustment similar to that in the engineer's level. It is 
therefore necessary first to make the axis of the bubble- 



10 



tube perpendicular to the vertical axis, and second to make 
the line of collimation parallel to the bubble-tube axis. The 
process of adjustment therefore is just the reverse of that 
used in the engineer's level. 

1. The Bubble-tube Adjustment. — Level the instrument 
carefully, especially over one pair of leveling screws. 
Revolve the telescope 180° on the vertical axis. If the 
bubble still remains in the center, the adjustment is perfect- 
If not, bring the bubble half-way back to the center by 
means of the leveling-screws, and correct the remaining 
half by means of the capstan-headed screws that give 
motion to the bubble-tube. Retest and repeat the adjust- 
ment until correct. 

2. The Collimation Adjustment: Peg Method. — The ob- 
ject of this adjustment is to make the line of collimation 
parallel to the axis of the bubble-tube. The adjustment is 
accomplished by means of the ''peg" method as follows: 

On ground that is approximately level, select or set two 
firm points at a distance apart equal to about 300 feet (d in 
figure 1). This distance may be paced. Set the level up 
midway between the points in the same horizontal line. 
Read the rod held on each of the points A and B (fig. 1) to 
thousandths, being careful always to have the bubble in 
the center of the bubble-tube whenever a reading is taken. 
Since A and B are equally distant from the instrument, all 
errors due to maladjustment as well as the effect of the 
curvature of the earth and refraction, are eliminated in sub- 
tracting the rod readings to determine the difference in ele- 
vation between A and B. Hence the difference of rod read- 
ings on A and B will be the true difference in elevation 
between A and B. Now set the level up at a point D in 
line with A and B and at a distance BD equal to one-tenth 
of AB. Level the instrument carefully and read the rod 
held on B. Were there no curvature of the earth or refrac- 
tion to consider, the difference in elevation of A and B 
added (if B is higher than A) or subtracted (if B is lower 
than A) would give the rod reading on A. when the line 
of collimation is parallel to the axis of the bubble-tube. 
For accurate results, however, a positive correction must 
be made for the combined effect of curvature and refrac- 
tion. 

With the level at D, let: — rod reading on B — b: rod 

11 



reading on A = a ; true differenve in elevation between A 
and B = h (as determined with the level at C) ; and the 
correction for curvature and refraction = c. Then if the 
adjustment is perfect a = b±h+c. h will be positive if B 
is higher than A, and negative if B is lower than A. The 
error due to maladjustment in the distance AB will be 
a— (b±h-j-c). We must correct, however, for the distance 
AD which is - of AB, and the correction is 

10 

k = ^[a— (b±h+c) ] 

The correction for curvature and refraction, c, is 0.576 
feet in a mile and varies as. the square of the distance. 
This gives the correction for a two hundred foot sight, of 
0.001 ft., and for a three hundred foot sight, of 0.002. After 
the correct target setting has been found and the target 
set, keeping the bubble exactly in the center of the tube by 
means of the leveling screws, bring the horizontal cross- 
wires to cover the horizontal center line of the target by 
means of the capstan-headed screws controlling the reticule* 
being careful, meanwhile, to keep the upright wire vertical. 
In this way the line of collimation is made horizontal, and 
since the bubble is in the center of its tube, the bubble-tube 
axis is also horizontal, and hence the two lines are parallel. 

After this adjustment is made a new rod reading is taken 
on B, and the difference between the target setting on A 
and this new reading should be the same as the true differ- 
ence as determined from C. 

C— THE ENGINEER'S TRANSIT. 

By revolving the alidade is meant a motion of the instru- 
ment in a horizontal plane, or around the vertical axis. 

By transiting the telescope is meant a rotation of the 
telescope around its horizontal axis. This is sometimes 
called plunging the telescope. 

The telescope is said to be direct when the bubble-tube is 
under the telescope; reverse when the telescope is so 
turned that the bubble-tube is above the telescope. 

The objects of the adjustments of the transits are: (1) to 
make the alidade revolve in a horizontal plane; (2) to make 
the line of collimation perpendicular to the horizontal axis 
of the telescope; (3) to make the horizontal axis of the 



telescope perpendicular to the vertical axis of the instru- 
ment; (4) to make the axis of the bubble-tube parallel to 
the line of collimation, thus enabling the instrument to do 
leveling; and (5) to make the vernier of the vertical circle 
read zero when the bubble is in the center of its tube. 

Adjustments 2 and 3, when correct, cause the line of 
collimation to generate a vertical plane through the axis of 
the instrument when the telescope is revolved on its 
horizontal axis. 

1. The Plate-bubbles Adjustment. — Set the instrument 
up firmly and bring the plate-bubble tubes parallel to the 
two sets of leveling-screws. Level the instrument carefully 
and revolve the alidade 180°. If the bubbles still remain 
in the center of their respective tubes the instrument is in 
adjustment. If not, correct one-half the error by means of 
the leveling screws and the remainder by means of the 
capstan-headed screws at the ends of the bubble tubes. 
Retest and repeat until correct. 

2. Line of Collimation Perpendicular to Horizontal Axis 
of Telescope. — This adjustment being accomplished, the 
line of collimation will generate a plane when the telescope 
is transited about its horizontal axis. Set up the instru- 
ment on nearly level ground where a good view may be 
obtained in opposite directions. Some 300 or 400 feet away 
set a definite point, as a nail partly driven in the top of a 
stake. Call this point A. Sight on this point with telescope 
direct and clamp. Transit the telescope and set a point in 
the line of sight some 300 or 400 feet in the opposite direc- 
tion. Call this point B. Unclamp the main motion and 
revolve the alidade until the telescope (now reversed) 
sights point A. Clamp and again transit the telescope. If 
the adjustment is perfect, the line of sight will now cut 



point B. If not set a third point, C, beside point B. Meas- 
ure the distance CB, and set a point, D, one-fourth of the 
distance CB from C, the last point set. Bring the line of 
Bight to cut this point D, by moving the reticule, which 

13 



carries the cross-wires, laterally; being careful at the same 
time to keep the upright wire vertical. Retest the adjust- 
ment and repeat until correct. 

3. Horizontal Axis of Telescope Perpendicular to Axis of 
the Instrument. — This adjustment following upon adjust- 
ment 2. will cause the plane generated by the line of coili- 
mation. when the telescope is revolved about its horizontal 
axis, to be a vertical plane. With the telescope direct, the 
instrument near some high point, a tall building preferably, 
sight some fixed point, at as high an angle of elevation as 
possible, and clamp the horizontal motion of the instru- 
ment. Turn the telescope down and set a point on a level 
with the telescope. Revolve the alidade, transit the tel- 
escope, and again sight the high point. Again plunge the 
telescope to the horizontal. If the adjustment is perfect, 
the line of sight will now cut the first point set. If not, 
set a second point beside the first. A point midway be- 
tween these two is in the same vertical plane with the high 
point. Turn the tangent screw and sight this middle point, 
then turn the telescope up until the high point appears to 
one side of the line of collimation. Correct the adjustment 
by raising or lowering the adjustable end of the horizontal 
axis until the vertical crosswire cuts the high point. Care 
must be taken to keep the horizontal plate level during this 
adjustment. Retest the adjustment and repeat until com- 
plete. 

If this adjustment is badly out the second adjustment 
must be repeated. 

4. The Telescope Bubble Adjustment: Peg Method. — 
This is accomplished in just the same manner as the 
Bubble Adjustment of the engineer's Y level. See adjust- 
ment 2, Engineer's level. 

5. Vertical Circle Vernier. — The vertical circle should 
read zero when the telescope bubble is in the center of its 
tube. Bring this bubble to the center, and if the vertical 
circle vernier does not read zero, loosen the screws which 
hold the vernier in place and give the vernier a lateral 
motion in the proper direction to make it read zero. In 
retightening the screws (which pass through elliptical 
holes in the standards) be careful that the vernier is close 
up against the vertical circle. 

14 



The first three adjustments are necessary for angular 
work in a horizontal plane. If angles are to be measured 
in vertical planes as well, the fourth and fifth adjustments 
are necessary. These adjustments are also necessary if 
the transit instrument is to be used as a level. 

D.— THE SOLAR TRANSIT (Saegmuller Attachment). 

The five adjustments of the engineer's transit as given 
above must first be very accurately made. 

1. Polar Axis Adjustment. — The object of this adjust- 
ment is to make the polar axis perpendicular to the plane 
containing the main telescope axis and the line of collima- 
tion. Level the instrument carefully and bring the large 
telescope bubble to the middle of its tube. The line of 
collimation and the horizontal axis of the main telescope 
now lie in a horizontal plane. The polar axis then is to be 
made vertical. Bring the small telescope over one pair of 
the small adjusting screws at the base of the polar axis 
and level the bubble on the small telescope. Revolve the 
small telescope about the polar axis 180°. If the adjust- 
ment is correct the bubble will still remain in the center. 
If not, correct one-half the error by means of the small 
adjusting screws at the base, and the remaining half of the 
error by moving trie small telescope. In using these adjust- 
ing screws, remember that they are exactly analagous to 
the leveling screws of the main instrument. When the 
bubble has been correctly adjusted over one pair of these 
screws, repeat the operation with the small telescope over 
the remaining pair. The adjustment is then complete. 

2. Collimation Adjustment of Small Telescope. — The 
object of this adjustment is to make the line of collimation 
of the small telescope parallel to the axis of the attached 
bubble. Carefully level the bubble under the large tel- 
escope. Place the small telescope in the same vertical 
plane as the line of collimation of the large telescope and 
carefully bring the bubble on the small telescope to the 
center. The axis of the large telescope bubble, the main 
line of collimation, and the axis of the small telescope 
bubble are now parallel, the small telescope being clamped 
in both motions. Unclamp the horizontal axis of the large 
telescope and with the large telescope sight some definite 
fixed point at some distant object (not less than half a mile 

15 



away). Now sight through the small telescope and see it' 
the central intersection of its cross-wires covers the same 
point sighted by the large telescope. If not, move the 
reticule of the small telescope until this condition of 
affairs obtains. Care must be used not to move the small 
telescope about its horizontal axis in making the adjust- 
ment. Retest and repeat until the adjustment is complete. 

E.— THE SOLAR COMPASS. 

1. The Plate-bjbbles Adjustment. — This adjustment is 

accomplished in the same manner as the similar adjust- 
ment for the engineer's transit. See Engineer's Transit, 
adjustment 1. 

2. Adjustment of the Lines of Collimation. — Each end of 
the declination arm has a lens and a disk, thus establishing 
two lines of collimation. The object of this second adjust- 
ment is to make these two lines of collimation parallel. 
They are made parallel to each other by making each of 
them parallel to the faces of the blocks containing the 
lenses and disks. To accomplish this the declination arm 
is removed and laid upon an auxiliary frame, called an 
adjuster, which is attached to the instrument in the place 
of the declination-arm. Having the latitude-arc and the 
declination-arc set approximately for the given time and 
place, lay the declination-arm upon the adjuster and bring 
the sun's image upon the disk. Carefully turn the arm over 
(on its longitudinal axis) and see if the sun's image still 
remains between the equatorial lines of the disk. If not, 
adjust the disk for one-half the error, and repeat the above 
operation for a check. Having thus adjusted one line of 
collimation parallel to the block faces, turn the arm end 
for end, and in a similar manner adjust the other line of 
collimation. The two collimation lines are then parallel to 
each other. 

3. Adjustment of the Declination-Arc. — The object of 
this adjustment is to make the declination-arc read zero 
when the lines of collimation are at right angles to the 
polar axis. Set the vernier of the declination-arc to read 
zero and by any means center the image of the sun upon 
the disk. Turn the declination-arm about the polar axis 
through 180° and see if the sun's image now falls exactly 
on the other disk. If not, move the declination-arm by 

16 



means of the tangent-screw until the image is exactly 
centered on the disk. Read the declination-arc, loosen the 
screws in the vernier-plate, and move the declination-arc 
back until it reads one-half of the total displacement from 
the zero reading. Center the image again, reverse 180°, 
and retest. Should the vernier be not adjustable, one-half 
the total displacement is the index error and should be 
taken into account in all the settings of the declination-arc. 

Adjustments 2 and 3 should be made within one or two 
hours of noon. 

4. Adjustment of the Latitude-Arc. — The error due to 
any maladjustment in the latitude-arc is of importance only 
when the true latitude of any given place is set off on the 
instrument, or w^hen the solar compass is to be used to 
determine the true latitude of any place. In making the 
adjustment, therefore, the latitude must be known. It may 
be obtained from a transit or sextant observation, or, 
roughly, from a good map. A few minutes before noon set 
up the compass having the sun's apparent declination set 
off for the given day and hour. Bring the lines of collima- 
tion upon the sun having it clamped at the twelve hour 
angle, and follow the sun by moving the tangent screw 
on the latitude-arc and by turning the instrument about its 
vertical axis. When the sun is at culmination, that is, has 
attained its highest altitude, read the latitude-arc. If this 
does not give the same value as the known latitude, move 
the vernier on the latiude-arc until it reads the true lati- 
tude. If the vernier is not adjustable, the difference 
between the known latitude and the vernier reading is the 
index error. 

If, however, we do not desire to use the instrument to 
determine latitudes, this error will have no effect, provided 
that the latitude used with the instrument be that obtained 
by it in the above observaion. Therefore always use the 
instrument with the latitude as given by it in a meridian 
observation on the sun. 

F.— THE PLANE TABLE ALIDADE. 

In making the adjustments of the plane table alidade it 
will greatly facilitate matters if it is borne in mind that the 
plane table may be considered as a transit in which the 
horizontal plate is replaced by the table-board. Instead, 

17 



therefore, of measuring horizontal angles, and plotting them 
afterward, we plot the angle at once. 

1. Adjustment of Leveling Bubbles. — If the alidade have 
two bubble-tubes set at right angles to each other, the 
adjustment is similar to that of the plate-bubbles in the 
transit. Level the plane-table with the alidade set along 
a given line on the plane table sheet. Now place the 
alidade along the same line but with the telescope pointing 
in an opposite direction. If the bubbles do not remain in 
the centers of their respective tubes correct one-half the 
error by means of the adjusting screws at the ends of the 
bubble-tubes and the remaining error by means of the 
leveling device. 

If the alidade have a single universal bubble (a spherical 
tube) the adjustment may be made in the same manner, 
taking components of the movement of the bubble in two 
lines at right angles to each other, and correcting half 
the error of displacement in each of these lines by means 
of the adjusting screws which fasten the bubble-tube to 
the alidade ruler. 

2. The Bubble Adjustment: Peg Method. — The intersec- 
tion of the cross-wires being placed (by eye) in the center 
of the field of view, the line of collimation is approximately 
in the axis of the telescope tube. The object of this adjust- 
ment then is to make the axis of the bubble-tube parallel 
to the line of collimation. This is done in exactly the same 
manner as adjustment 2 of the engineer's level. 

3. Horizontal Axis of Telescope. — This adjustment is 
exactly analagous to adjustment 3 of the engineer's transit. 

PART II. 

FIELD PROBLEMS. 

PROBLEM I. 

Chaining between fixed hubs on a slope. 

Equipment: — 1 chain (Engineer's or Gunter's) eleven 

marking pins, two range poles, and two plumb-bobs. 

Directions: — Select a course over a considerable and 
variable slope and from 12 to 14 chains in length, fix the 
range poles, one at each end, and find as near as possible 
the correct horizontal distance between the points selected. 
Measure the distance at least twice in each direction with 

18 



each man as head-chainman; this will give at least two 
results obtained under similar conditions. 

Method: — One pin is stuck at point of beginning of the 
course, to be removed by the rear-chainman when the next 
pin has been set one full chain length away. The rear- 
chainman should first give the alignment to the head- 
chainman, aligning by eye, and then give his undivided 
attention to keeping his end of the chain exactly at the 
proper beginning of measurement for that chain length. 
The alignment having been given, the head-chainman will 
mark it approximately on the ground, then keeping the 
chain in that line, pull it with a steady pull strong enough 
to eliminiate the effect of sag, and stick a pin vertically 
under the end of the chain. Avoid jerking the chain at any 
time. The man at the down-hill end of the chain, whether 
head-chainman or rear-chainman, should find the elevation 
at which to hold his end of the chain that w r ill give the 
longest slope distance between his plumb-bob point and 
the other end of the chain, i. e., hold his end of the chain 
level with the other end. Two or three trials on any slope 
will give the proper height at which to hold this end of the 
chain, the other end should be held firmly against the 
ground or person of chainman to "steady" the tension on 
the chain and thus make easier the task of bringing the 
plumb-bob to rest at the proper measure just clear of the 
ground. Only in case that the measurements at both ends 
of the chain are on ground lower than some point in line 
between them, is it allowable for both chainmen to use 
plumb-bobs simultaneously. Should the slope be steep 
enough to make it necessary to "break chain," the chain 
should first be drawn out to its full length, the head- 
chainman returning to such point as is necessary to make 
level that portion of the chain used, and measurement 
made. The next measurement should then be made with 
the next portion of the chain, and so on until all is used, 
the rear-chainman surrendering to the head-chainman all 
the pins used in marking the sub-chain lengths. In making 
oi giving a measurement, the chainmen should always 
stand facing at right angles to the direction of the chain 
in order to accurately see when the end of the chain or the 
plumb-bob point is vertically over the point given or sought. 
At the end of ten chain lengths the rear-chainman has ten 
pins which he now gives to the head-chainman, a "tally" 

19 



is made, and the measurements proceeded with as before, 
to the end of the course. The total distance between ter- 
mini should be recorded, in feet and tenths, if an engineer's 
chain is used, and in chains, links, and tenths of links, if a 
Gunter's chain is used. 

Form of Notes. 



. neau tri 

— RearCfr. 


Problem *l 


dug 27 04 


From 


To 


Di'sr: 


Slope 






*A 


#r 


£4314 


uA 








#R 


* A 


£43„.9 


Dawn 








#A 


* B 


64 3 A 


Up 








#n 


* A 


644,1 


Down 






Mean 


643,6 




\ 



PROBLEM II. 

Laying out Rectangular Field and Chaining around 
Obstacles. 

Equipment: — 1 chain, 11 marking pins, 2 line rods, and 
2 plumb-bobs. 

1. Select an area, where a rectangular figure may be 
laid out with dimensions of from three to five chain lengths. 
Run out a series of courses ab, be. cd. de, laying out right 
angles at b, c, and d, successively by the "3, 4, 5 method." 

This is best done, if you have a 
a 50-ft. chain, by finding a point 
g, in the line ab, 15 ft from b, 
then with one end of chain at g 
and the 45-ft. link at b pull each 
portion of the chain taut with 
the 25-ft. mark at h and set a 
pin at h. It may also be done 
by making bg = 30 ft. and with a 
radius bh = 40 ft. describe a 
small arc through h and then 
with gh = 50 ft. locate h. Pro- 




20 



duce the direction bh on to c and repeat, until finally* e is 
reached, paying no attention meanwhile to the location of 
a. Note the location of e with respect to a in distance and 

distance ea 
direction. Error of closure =—-— — . — — 

total perimeter abcde 

2. Chain around an imaginary obstacle as shown in 
sketch, making the angles at b, c, d, and e 90° then produce 
fe backward, measure and note the distance eb', bb', and 



be and de may 
be made 50 ft and 
cd not less than 
100 feet. 




Note. — If you have a Gunter's chain, for feet, above, read 
links. Sketches with statements of results will consti- 
tute a sufficient report. 

PROBLEM III. 
Measuring the Angles of a Closed Figure. 
Equipment: — 1 chain, 11 marking pins, 2 line rods, and 2 
plumb-bobs. 

Select or set 
five stakes in 
the form of a 
pentagon, no side 
of which is less 
than three chains 
in length. Meas- 
ure all the angles 
by the method 
shown in sketch. 
If x be made 50 
ft. then y divided 
by 100 will = sin 
y 2 A, thus sim- 
plifying the nu- 
merical work. 




Should any angle largely exceed 90° produce one of the 
adjacent sides and measure the exterior angle, i. e., as at 
e measure angle fea. 

Measure the length of each side, and after assuming 
one side as a meridian, calculate from the measured angles 
the bearing of each course. The length of a course times 
the sine of its bearing is the longitude difference, and 
times the cosine, is the latitude difference of that course. 
The algebraic sums of the longitude differences and latitude 
differences are the errors in long, and lat. which let = u and 

v. Error of closure = 

perimeter of field 







Form 


of Notes and Calculations 




5fa. 




%A 


A 


Bearing 


Plfit- 


L«h 

Difference 


Long. 
Difference 


i 


0.734 


47° 14' 


34° 2 8 


x— ^ — 
















N.fissumed 


• ffi%3 


+ I&7.3 


O 


? 


0.755 


43°o2' 


38° 04 


















N.8I°S6'E. 


133^ 


+ 27- 2 


+ 191.7 


3 


03/3 


54° 23 


108°46 


















S.2£° 50 E. 


18\* 


-\G\3 


+ &1.9 


4 


0.612 


31° 45 


IIG°30 


(Sufi 
















S.3G°40W. 


70J 


-56* 


-4/9 


5 


04&8 


29° 13 


I2I°34- 


(Supl) 
















N84° 54W 


234? 


+ 20? 


-233. 3 


/ 






533° 22' 






+ 2/5\ 3 


+273.6 








540 00 






-£/<?•' 


-275* 



Error = -0°3S' -f 2. 8 + \£ 

Error of closure - tCZSP+OQ'* - J_ ^ 1 f n J 80 
846.4 380 ** ' JdU 

Note. — As in Prob. I if you have a Gunter's chain for feet 
above read links. 



PROBLEM IV. 

Rod Reading and Target Setting with Level. 

Equipment: — Level, — Philadelphia level rod with target. 
1. Set up level in some locality where the rod may be 

22 



plainly seen when held upon some firm point of rock or 
stake a distance of from 250 to 300 feet from the level. 
After rather closely leveling the instrument focus the tele- 
scope upon the rod, then accurately center the bubble and 
direct the setting of the target by the rodman. (Be careful 
to give no signal for "all right" after setting the target 
or taking a rodreading until after making sure that the 
bubble is still well centered.) The rodman will then read 
the setting of the target to the nearest 0.001 foot and 
record that reading and then move the target a few inches 
up or down. The target should then be again set, read 
and moved until a series of at least 10 readings have been 
recorded. 

2. Turn the rod so that the back is toward the leveler, 
then as the rod is extended a little at a time the leveler 
may read the various values at the crosswire intersection. 
These readings will have no relation to the elevation of 
bottom of rod — they are simply values determined by 
readings which should vary from one another by the 
amount of rod extension between the times those readings 
were taken, testing the accuracy of the leveler in leveling 
his line of sight and reading the rod. 

The leveler will read the rod as a "speaking rod" to the 
nearest 0.01 foot and record each reading until at least 
10 values are obtained. After each reading the leveler will 
signal the rodman, who will read the rod to the nearest 
0.01 foot and record the total amount the rod is extended 
at that time, and then extend a different amount and hold 
up for a new reading. 

3. Repeat Part 1 at a distance of about 500 feet. 

Form of Notes. 



Mean 4.764 



~w% 



0000067 





B? 


rt I 






Obs. 


Thrqet 


A 


d 2 


f»TO- 


/ 


Z.7Z3 


aool 


o.oooool 


° n-f 


2 


4JC>\ 


ao'oz 


9 


% fO.000087 =Q0 02 


3 


AJQJ 


O.O03 


9 












-- 














d— difference between each observation and the mean of 
all the observations. 

n=number of observations. 

E=probable error of a single observation used as a meas- 
ure of precision. 





Pa 


rt H 








^ 1 ^? d 

0b5.T?ecidinq 


Rbd 
Extension 


DffF. j A 


d 2 




1 A7.9 


o 


*7 q 1 1 




2 


XJtf 


O.OR 


Z.RO i 






3 


8SG 


OAJ 


8.79 ! 






A ' 


9. OS 


O.Z9 


8.79 1 






-- 







-—I 


' 





PROBLEM V. 



Differential Leveling. 

Equipment. — Level, levelrod and hatchet, with a few 
stakes for turning points if needed. 

Starting at Bench Mark # 1 find the elevation of some 
other designated Bench Mark; then complete the circuit 
uy returning to point of beginning. You should close on 
B. M. # 1 with an error not greater than 0.03. A sight 
taken upon a rod held on a B. M. or turning point (T. P.) 
for the purpose of finding the elevation of the line (H. I.) 
is a plus "sight" and a sight taken when the H. I. is 
known for the purpose of finding the elevation of the 
point on which the rod is held is a "minus sight," for the 
line of sight of the instrument must always be higher than 
the bottom of the rod by the amount of the rod reading. 
Then if either the H. I, or the elevation of B. M. or T. P. 
is known the other may be found. See also Raymond's 
Surveying Art, 35. So choose the places for setting up 
your level that the length of both sights from that place 
will be as nearly equal as possible, in order to eliminate 
any error of adjustment that there may be in the instru- 
ment. All turning points should be firm and preferably 
with a convex upper surface like a projecting knob of well 

24 



imbedded rock in a gutter or a stake firmly driven in 
the ground with its top nearly flush therewith. Never use 
the surface of the ground itself or a loose rock on it. 
When starting to return from B. M. X reset the level and 
get an entirely new reading for the + sight from X instead 
of using the reading that you obtained for the — sight 
upon X; this incorporates X into the circuit B. M. # 1 to 
B. M. # 1. 

To check your numerical work upon completion of the 
problem, find the sums of all the + sights and — sights. 
These sums will differ from each other by the amount you 
lack in closing ou starting point. 





Form of Notes. 




Stn. 


+ s. 


H.L 


-5. 


Elev. 


RM*I 


2J6 


344.69 




34133 


TP 1 


a 39 


333 r 47 


11.61 


333 OB 


TP 2 


9.£3 


33224 


I0.8G 


322.61 


Z7? 3 






0.7/ 


331.53 




/o7q 




""> i in 


i A! Qi 




1 clJ 




l n 7 3 


1. 3 / 4"? 




7") 'CC A 




/ (LJO 


JO/- J*J 

//i An 




DitF. it) civv. — 


1 Vrtu 


1 U/tU 



Leveler will read the rod to nearest 0/01, not using the 
target. 



PROBLEM VI. 
Profile Leveling. 

Equipment: — Level, levelrod, hatchet and a few stakes 
tor turning points if needed. 

Starting at B. M. # 2 run a line of levels southward 
between East Hall and the Library to the road running 
in front of the Botany building, thence following the 
middle or edge of road westward to South Hall, thence 
northward to opposite North Hall and thence eastward 



along the path to point of beginning. The rodman will, 
pace off and report to the leveler the distance from point 
of beginning to sight taken. Each even 100 feet is called 
a station and any fractional part of a station will be re- 
corded as + so many feet, e. g. 300 feet from beginning 
point is Station 3 and 45 feet beyond Station 3 will be 
3 -f- 45. The rod should be held on the ground at each 
station and at every place between stations where there 
is a decided change in direction of slope of the ground 
in the line followed. The rodman will also select turning 
points as often as directed by leveler as in problem 10. 
As these tunring points are merely for the purpose of 
giving the new elevation of the line of sight of the level 
at the next set up, no record need be kept of their location- 
Care need only be taken that each T. P. is firm and so 
chosen or set that the rod held on it will be clearly cut 
by the line of sight of level from its location on either 
side of it. Read the rod to nearest hundredth of a foot 
on T. P.'s and B. M.'s and to the nearest tenth only when 
the rod is held on the ground. Check on B. M. # 3 when 
passing it. Plot the profile on profile paper (Plate B), 
using 100 feet to the inch horizontal and 15 feet to the 
inch vertical. 







Form of 


Notes. 






Sta 


-KS. 


HL.L 


-5i_ 


Efer- 




B.M*2 


0.63 


fOO.63 




lOO.OOjt 


Issumedj 


1 






ffl 


pm-.r v 




+ Go 






a.3 


92.3 




¥ 70 






fL6 


92.0 




T.P *i 


nja 


90.Q4- 


1137 


flq.?6 




2 






L4- 


fl.q.6 




3 






fl.7 


8A3 




T.P *2 


U6 


8039 


IOM 


79.23 




3 +3S 






2./ 


783 




etc. 






etc. 


etc. 





26 



PROBLEM VII. 
Adjustment of Level. 

Equipment: — Level (not in adjustment) and levelrod. 

Put the instrument given you into perfect adjustment., 
consulting one of the instructors, after making each ad- 
justment, otherwise no credit will be given for the prob- 
lem. Proceed as indicated in A, part 1, if you are given 
*i Y level, or as in B if you are given a dumpy level, making 
use, preferably, of the roadway east of North and South 
Hall, selecting a somewhere opposite North Hall and b 
north of a about 300 feet. 

For Notes. — Write a concise statement of what you do in 
making each adjustment, together with notes taken in 
making Peg adjustment. 

PROBLEM VIII. 
Rodsetting and Vernier Reading Practice with Transit. 
Equipment: — Transit, linerod and tape. 
Part I. Set up where there will be a clear view of the 
rod held on a board or cement walk about 500 feet dis- 
tant from the instrument, bisect the rod as close to the 
walk as possible and clamp both limb and alidade. The 
rodman will mark this initial position of the rod and then 
move the rod a short distance to the right or left and is 
again lined in by the transit man. A record is made of 
the magnitude of the error of lining the rod and its direc- 
tion from the initial position. Repeat until ten such read- 
ings have been made. Compute the probable error of a 
single sighting and reduce it to its angular value. 

Part II. With the transit sighted again upon the rod 
held at the initial point, the transit man reads vernier A. 
Now move the rod to one side, as in Part I, and turn the 
alidade a small amount one way or the other and again 
bring to the same reading as before, and again line in 
the rod as in Part I. Repeat until ten values have been 
obtained. As the vernier reading is to be the same lor 
all settings, the error of both setting the vernier and of 
aligning the rod will appear at the rod in Larger or smaller 

distances of each setting from the initial point. 



Compute the probable error as in Part I. 



(paced) 


No.ofSet 


Distfrom 
Initial Pfc 


d 


d 2 






o 


n 






d- each obsGyv— 




J 


Rnr+rio? 


O.04S 




ar'tth. mean of 
a/I the obs. 


5oo 


2. 


Lor- 0.04 


n.ois 






etc.. 










10 


-0.03 


0.005 




z,=%m 






-AflW 


"ZfsJ? 


1- 




Mean 


= -O.OZ5 


<£-{p / 




£-r =fan°< or 










j^/o/ 


cK-fa; 


^'soo 


aooooos-tan 1" 
PROBLEM 


or 0.000017= fan. 0?OOl 
IX. 



Angle Reading Practice, Multiplying Angles. 
Equipment: — Transit and plumbbob! 

Set up the transit over a designated hub and measure 
the angle by repetition between the two directions instru- 
ment to X and instrument to Y, X andY being sharply 
denned points also designated. Clamp the alidade, then 
turn the limb and set the vertical cross-wire on the left- 
hand point X. Read and record the readings of both ver- 
niers A and B, leaving out of the record the full degrees 
as read on vernier B. Take the mean of the fractional 
parts of a degree as read on vernier A and vernier B, and 
this, with the whole degrees from vernier A, will constitute 
the mean value of the reading. 

Now loosen the alidade clamp, turn to and set the line 
of sight on the right hand point Y, and again find and 
record the mean of the vernier readings. The difference 
between the two means of vernier readings is the first 
observed value of the angle measured. Unclamp the limb 
and again sight on X, being careful to not disturb the 
alidade clamp or tangent screw, then clamping the limb, 
unclamp the alidade and again sight on Y, obtaining a 
second value of the angle. Proceed thus until five values 
of the angle have been obtained, then plunge the telescope 
and repeat in the opposite direction. 

28 



As each turning- of the instrument from Y to X is made 
about the axis of the limb only, the readings of the ver- 
niers remain constant from any pointing to Y to the next 
succeeding pointing to X, therefore after the first reading, 
no other readings of the verniers need be made when the 
instrument is pointed to X. 

Compute the probable error. 

Form of Notes. 



Verily 


''?• 


Mean 


Value of 
Angle 


d 


d 2 


86W 


r.17 


8G°M0 








1 / 2.3o 


,3/ 


1 \ 2.305 


?.£\35 


O°oo2 


,oooc)04 


138.43 


.44 


138A35 


26.130 


,oo3 


9 


\G4.57 


.57 


l£4S7n 


2CMS 


.ooZ 


4 


I °>0.70 


70 


1 30700 


1GA30 


.003 


3 


efc. 






_ 




_ 


34150 


So 


347-500 


26.130 


.0 03 


9 






' 86J70 


M^2G \33 


^V= 




lo) 


2 G 1.330 




• 



16.133 
X = Spire at S.W. Cor Els worth 

Sf and ahfon Way 
Y = Spire of Conservatory 



^-%rw 



E^ =M± ^Probable error 
of the mean 



PROBLEM X. 

Traversing with a Transit. 

Equipment: — Transit, line-rod, plumbbob, hatchet and 
stakes. 



Set hubs with points, in an approximately equilateral 
pentagon, preferably choosing such a location for each 
that the bottom of a line-rod held oil it may be clearly 
seen from the 1 next hub in each direction. Set these hubs 

29 



aot closer than 200 feet apart. Set up the transit over one 
hub, lower the compass needle and after setting vernier A 
to read 0, turn the whole instrument until the telescope, 
direct, points South; i. e., the north end of the needle will 
read South. Clamp the limb and loosen the alidade, then 
sight to sta. 2 and read the azimuth on vernier A and the 
bearing at the north end of the needle. At sta. 2 set off 
on vernier A the azimuth of the line from sta. 2 to sta. 1 
(this will differ from that from sta. 1 to sta. 2 by 180°), 
sight to sta. 1, clamp the limb and read the needle. This 
needle reading should check with the forward bearing from 
sta. 1 unless there is local attraction at either of the sta- 
tions. Now unclamp the alidade and sight to sta. 3 and 
read vernier and needle. Proceed similarly at stations 3, 
4 and 5, and then again occupy sta. 1 orienting tm sta. 5, 
check the azimuth on sta. 2. This should be the same as 
that obtained at first, or at most should not vary more 
than 0°.03 therefrom. Each time a needle reading is 
taken see that it agrees with the azimuth as read on ver- 
nier A at the same time. 

Form of Notes. 



Inst. 
at 


Pointing 
To 


Vern.A 


Needle 


A 1 


S 


ofoo 


South 




A 2 


347.63 


S.\2°4-E. 


A 2 


A / 


/6 7.<£3 


NJ7°.OW. 




A 3 


S(o Jfl 


SL SU to. 


A 3 


A 2. 


? 36.18 


N.S62W. 




A A 


I&L31 


N. IASW. 


A4- 


A 3 


3 A 1.37 


5. 183 S. 




&5 


2.13.7/ 


N 33 Jr. 


A5 


A*r 


33,7/ 


S.33.7W. 




A / 


Z85.C4- 


S. 75.0 El 


Al 


^ 5 


\ 05.04 


N.75J)W 




/\Z 


34U4- 


S.I2AE, 


(froi 


77 above) 


3*763 





error of closure- o.o\ 



30 



PROBLEM XI. 

Transit Adjustment. 

Equipment: — Transit (not in adjustment) and line-rod. 

Make the first three adjustments of the instrument given 
you as indicated in C Part 1, making use of the roadway 
east of North and South Halls. Consult one of the instruc- 
tors after making each adjustment, otherwise no credit 
will be given for the problem. 

For notes write a concise statement of what you have 
done in making the adjustments. 



PROBLEM XII. 

Determining the Value of f/i by Stadia Reading. 

Equipment: — Transit, plumbbob, stadia-rod, 50 foot tape 
and marking pins 

Set up the transit where there will be a clear and com- 
paratively level sight for 500 feet. Measure the instru- 
mental constant f^c and lay it off on the ground, measur- 
ing from the plumbbob. From this as a zero point meas- 
ure in the same direction a distance of 500 feet, marking 
each hundred feet station. With the rod held in turn at 
each of these distances, read the upper, low r er and middle 
crosswires. Test the wire intervals by turning the tan- 
gent screw of the vertical circle enough to bring the cross- 
wires to a slightly different position on the rod. Make 
five readings at each distance and take the mean of the 
five as the wire interval for that distance. All the read- 
ings should be taken with the line of sight very nearly 
level (say within a degree of level). From the observa- 
tions compute the value of f/i. 



31 



Form of Notes. 



Obs. 


Upper Lower 
Wtre. IntervaMire Interval 


Tota\ 
Internal 




// 


Oi5oo 


OA90 


0390 




at 2 


OJiOO 


O.A35 


0395 




\00\ 3 


0*5o5 


OA95 


LOOO 




u 


0.500 


0^90 


0390 




[ 5 


O.500 


n&95 


03^5 










4-370 


Mean = d.394- 


rl 


LOOO 


O.990 


I 990 


ffc = IOOJ&03 


J2 


l.nio 


0390 


? t nnn 




Zoo) 


3 


J r nn5 


0.995 


2,non 






4 


i,om 


LOOO 


2/0/0 




l 5 


LOIO 


0.330 


2.000 










10.000 


Mean^2o00 


etc. 


etc. 


etc. 




ft =100-000 



PROBLEM XIII 



Traversing with the Stadia. 

Equipment: — Transit, plumbbob, stadia-rod, hatchet and 
stakes. 

Make a traverse of a five or six sided figure as in Prob- 
lem X, measuring the distances between stations with the 
stadia. Find the difference in elevation of successive sta- 
tions and see that the algebraic sum of all these differences 
is equal to zero. Distances and vertical angles should be 
read in both directions along every course, in order to check 
the reading and to eliminate instrumental errors. Compute 
the horizontal length of each course and the error of 
closure of the field. Horizontal distances should be to the 
nearest foot and the differences in elevation to the nearest 
tenth of a foot. 

32 



Inst 
at 


Pointing 
to 


Azlm. 


Needle 


Pfsf. 


Vert 

Angle 


IfflF. 

in El^u 


Hor. 
Dfsf. 


fk^. 


D \ 


South 


o° 1 South 














P 2 


235*6 j/Y55°9£. 


26/ 


-/°V) 








n 2 


O / 


5536LS.56.6W 


26/ 


W..W 










D 3 


/ 73.22 1 AC £7 W 


227 


-3.76) 








a 3 


o 2 


5?53.22 q 6.3 £ 


??£ 


+-3#J 










□ A 


.97-63 /V/8241^ 


?78 


V-504) 








D A 


D 3 


277^3 


etc. 


etc 


e/fc/ 










e.tc. 

















Form of Notes. 



PROBLEM XIV. 



Plane-table Practice: — Two Point and Three Point Prob- 
lems. 

Equipment: — Plane-table, alidade, range-pole and a sheet 
of plane-table paper. 

Given two stations or landmarks, A and B, a known 
distance apart, and both points inaccessible, plot these 
points to scale on the paper and then locate on the paper 
a third point C, by resecting on the known points. The 
"Problem" is to oreint the table when occupying C so 
that the plotted ab will be parallel to AB on the ground. 
It will first be necessary to occupy some temporary sta- 
tion X and there turn the table until ab is approximately 
parallel to AB. With this approximate orientation, resect on 
A through a and on B through b; the intersection of these 
lines will be x', aud through that point draw a line toward 
C, and c' will be somewhere in that line. Move the table 
now to C and orient by sighting back along c'x' to X. 
then resect through a on A locating c' in the lir* 1 c'x'. 
Through c' sight to B, and the intersection of c'— B and 
x'b is b' and the line joining a and b' is exactly parallel to 
AB. With the alidade along ab' line in the range-polo 200 
or 300 feet away, then remove the alidade to the line ab 
and orient the table by sighting to the range-pole, ab 
is now parallel to AB. Resect through a and b respec- 

33 



tively on A and B and locate c. From c draw lines toward 
several points, such as trees, hydrants, building corners, 
etc., which will come within the limits of your plot. Re- 
move the table now to some fourth point D, and do the 
"three point problem.'' D must be so chosen that it is not 
in the same circle with A, B and- C. 

Proceed as follows: 

i. Place the alidade along cb. swing the table until B is sighted and 
clanip the table. 
3. Swing the alidade about c as a center and sight A. and draw ce. 

3. Place the alidade along be and swing the table until C is sighted and 
clamp the table. 

4. Swing the alidade about b as a center and sight A, and draw be. 

5. Draw Aae. This line, produced, if neeessar\', contains d. 

6. Place the alidade along da (i. e., ea), swing the table until A is 
sighted and clamp the table. 

7. Swing the alidade about b as a center and sight B and draw bd. 
S. Swing the alidade about c as a center and sight C and draw cd. 
These three lines, ad, bd, and cd should meet at the point d, which is the 

plotted position of the point D. 

With d as a center resect on the same points sighted to from C, and 
locate them on the plot. 

Extreme accuracy in drawing is essential to good results. 

If D is chosen outside the circle ABC and there is time, 
try another solution of the problem, choosing D inside the 
circle ABC. 

The drawing, properly lettered and dated, will consti- 
tute a sufficient report. 




34 



PROBLEM XV. 



Azimuth Determination with Solar Attachment. 

Equipment: — Transit with solar attachment, and plumb- 
bob. 

Set up over a designated hub and by means of obser- 
vations on the sun determine the azimuth of a given base 
line. 

Good results may be obtained only from two to four 
hours before or after noon. Compute the declination set- 
tings for each half hour of the period of observations 
(do this preferably beforehand). Check all the adjust- 
ments of the solar attachment before proceeding with the 
observations. When ready to make a setting sight along 
the given base with the vernier reading zero, clamp the 
limb, loosen the alidade and point the telescope in a south- 
erly direction. Set off on the vertical circle the com- 
puted setting for that time and carefully level the tele- 
scope of the attachment. Now set the vertical circle to 
read the co-latitude of the place and find the meridian. 
This is done by turning the alidade slightly about the ver- 
tical axis of the instrument and at the same time revolv- 
ing the attachment about the polar axis until the image 
of the sun is exactly centered in the small telescope. The 
polar axis, and hence the line of collimation of the large 
telescope, is now in the meridian and the azimuth of the 
base may be read on verniar A. There are two sights on 
the small telescope, one small one near the objective end 
and a slightly larger one near the other end. Bring the 
shadow of the smaller of these sights to fall on the other 
and the sun will be found in the field of view of the solar 
telescope. 

Care should be taken that the vertical axis of the in- 
strument is exactly vertical, even more accurately than 
can be done by relying simply upon the action of tin 4 
plate-bubbles. Therefore complete the leveling of the plate 
with the bubble on the main telescope, turning the vertical 

35 



circle tangent screw and leveling screws until the bubble 
remains centered for all positions of the instrument. 

Note the reading, now, of the vertical circle vernier, and 
if not zero, it will be the index error to be taken account 
of when making the settings for declination and co-latitude. 
If the declination, corrected for refraction, etc., is nega- 
tive the objective end of the main telescope is raised from 
the horizontal when making the setting to the vertical 
circle, and lowered if the setting is positive. 

After each observation remake all settings in order to 
get entirely independent results. Obtain a series of at 
least ten determinations of the azimuth, checking back 
on the base at the close of the series to see that the ver- 
nier still reads zero. 



Form of Notes. 



Time 


s 


Eefr. Cok 


Peel. 
Setting 


Azim. 
of Base 


Needle 


2:00m. 


-h/7.^2 


0.°03 


+ IZ25 


347/6 


5 I2S E 










347/7 


etc. 










347/5" 












etc. 




2:3om 


+IZZ2S 


0.03S 


+ /Z26 


























cp=37 


'"7 










Y r-i w 1 




3100VM 


+ /Z2.3 


o.o4 


+17-27 



















36 



PROBLEM XVI. 



Azimuth Determination — Direct Observation on the Sun. 



Equipment: 

pi umb bob. 



-Transit with prismatic eyepiece, and 




Set up over a designated hub, measure the altitude of 
the sun and simultaneously read its 
azimuth from a given base whose 
assumed azimuth will be zero. Good 
results will be obtained only from 
two to four hours before or after 
noon. As the altitude and azimuth 
must be obtained at the same 
instant, some preliminary practice 
will be necessary before good obser- 
vations will be obtained. Point the 
telescope toward the sun, using the 
prismatic eyepiece if the sun is high. 

and the colored shade to protect the eye, lightly clamp 
both the alidade and vertical circle with the sun's image 
in the field of view. With a hand on each of the vertical 
and horizontal tangent screws, quickly bring the cross- 
wires simultaneously tangent to the sun's limb as shown 
in the diagram, read both altitude and azimuth and as 
quickly as possible turn the alidade through 180° and 
transit the telescope and repeat the operation, observing 
the sun in the opposite quadrant. Pairing observations this 
way has the effect of eliminating any error in collimation, 
index error of the vertical circle, and error of adjustment 
of the horizontal axis, and gives the altitude and azimuth of 
the center of the sun for the time midway between 
observations. This practice should be repeated until 
observations can be taken about a minute apart. Then 
obtain four or five pairs of observations from which to 
calculate the azimuth of the base. In the reduction of the 
observations use the mean of the observed values in each 
pair and reduce as a single observation. 



37 



















1-0 
















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-Jl z 



PROBLEM XVII. 

Base-line Measurement. 

A given base-line, AD, is so located that only the two 
A _B_ C n 




portions, AB and CD, can be measured with a tape. A 
point E, nearly at right angles to the base from B, is so 
chosen as to be intervisible with A, B and C, and giving 
angles AEB and BEG as nearly equal as may be to the 
angles EAB and ECB. With transit and tape, set points 
between A and B and between C and D slightly less than 
a tape-length apart, or at such shorter distances as will 
be found necessary in order to obtain correct slope dis- 
tances between successive points. Measure accurately the 
slope distances between A and B and between C and D 
at least twice in each direction. Run a line of levels over 
the base and find the elevation of each point to which a 
slope measurement was taken. Reduce the slope meas- 
urements to the horizontal and find AB and CD. With a 
transit measure each of the angles of the triangles ABE 
and BEC by the method of repetition, repeating each angle 
ten times. Adjust the values of those angles to the con- 
ditions, ABE-f EBC=180°, ABE-f-AEB + BAEr=180 °, and 
BEC+CBE + BCE=180°. 

With the adjusted values of the angles and the length 
AB solve the triangle BAE for BE and then BEC tor BC. 
Add AB, BC and CD and get the horizontal length of the 
base AD sought. 

Problems 1, G and 9 show forms of notes for the various 
parts of the field work. In the calculations, tabulate the 

39 



work in some neat, concise form, showing the results and 
checks, if any. 

PROBLEM XVIII. 

To Find the Position and Elevation of an Inaccessible 
Point. 

Measure (by the method of repetition) the horizontal 
angles at A and D, the extremi- 
ties of the base-line measured in 
problem XVII, between the base 
and a given point F, and calculate 
the distances AF and DF. When 
occupying A measuring the hori- 
zontal angle DAF, read also the 
vertical angle of D from the hori- 
zontal at each sighting of D, 
and the vertical angle of F from 
the horizontal at each sighting of 
F. Similarly at D, find the angu- 
lar distances in elevation of A and 
D, and F and D. Caluculate the 
difference in elevation between A 
and D, and compare with that ob- 
tained with the level in Problem 
XVII. Compute the elevation of F 
from both A and D by means of 
the vertical angles at those sta- 
tions, and compare the results. 

Check the foregoing triangula- 
tion by running a random stadia line from D to F and 
back to A. Red ace the readings and compute the hori- 
zontal distances DF and AF and compare with the results 
obtained by triangulation. Compare also the differences 
in elevation obtained by the two methods. 

Run a line of levels from D or A to F and return. Set 
bench-marks as often as every 80 feet difference in eleva- 
tion. Check within 0.02 feet between successive B.M.s 
and within 0.05 feet between extreme elevations. Com- 
pare these results with those obtained by the other 
methods. 

40 




I. — Latitude Coefficients to be Used With the 
Refraction Corrections in Declination. 



Latitude 


Coefficient 


Latitude 


Coefficient 


Latitude 


Coefficient 


o 














15 N. 


•30 


30 N. 


.65 


45 N. 


1.20 


16 


•32 


31 


.68 


46 


1.24 


17 


•34 i 


32 


•71 


47 


1.29 


18 


•36 


33 


•75 


48 


i-33 


19 


•38 


34 


.78 


49 


[.38 


20 


.40 


35 


.82 


5° 


1.42 


21 


.42 


36 


•85 


51 


i-47 


22 


•44 


37 


.89 


52 


1-53 


23 


.46 


3S 


.92 


53 


[.58 


24 


.48 


39 


.96 


54 


1 64 


25 


•50 


i 4 ° 


1. 00 


55 


1.70 


26 


•53 


i 41 


1.04 


56 


1.76 


2 7 


.56 


42 


1. oS 


57 


[.82 


28 


•59 


43 


1. 12 


5 s 


1 88 


29 


.62 


44 


1. 16 




f.94 


30 


.65 


45 


1.20 


60 


2.00 



41 



II. — Refraction Corrections to be Applied 



































J2 

K o S 

Q ° 




Jan. 


Feb. 


Mar. 


April 


May 


June 
























I 


I 


0.032 


0.024 


0.017 


0.011 


0.008 


0.005 


2 


2 


■037 


,028 


.019 


.013 


.009 


.006 


3 


3 


.051 


.036 


.024 


.016 


.011 


.008 


4 


4 


.104 


.058 


•034 


.021 


.015 


.012 


5 


5 






.076 


•037 


.024 


.019 


6 


1 


.031 


.023 


.016 


.011 


.007 


.005 


7 


2 


.036 


.020 


.018 


.012 


.008 


.006 


8 


3 


.049 


•033 


.022 


.015 


.010 


.008 


9 


4 


.098 


,053 


.032 


.020 


.014 


.012 


10 


5 






.066 


■034 


.023 


.019 


ii 


1 


.030 


.022 


.015 


.010 


.007 


.005 


12 


2 


•035 


.024 


.017 


.011 


.008 


.006 


13 


3 


.047 


.031 


.020 


.014 


.010 


.008 


14 


4 


.090 


.048 


.029 


.019 


.014 


.012 


15 


5 




•156 


.058 


.032 


.022 


.019 


16 


1 


.029 


.020 


.014 


.009 


.006 


,005 


17 


2 


•033 


.023 


.016 


.010 


.007 


.006 


18 


3 


•043 


.029 


.019 


.013 


.009 


.008 


19 


4 


.081 


.044 


.027 


.018 


.013 


.012 


20 


5 




.126 


.051 


.029 


.021 


.019 


21 


1 


.028 


.019 


.013 


.009 


.oo5 


.005 


22 


2 


.032 


.021 


.015 


.010 


.007 


.006 


23 


3 


.041 


.027 


.018 


.012 


.009 


.008 


34 


4 


•073 


.040 


.025 


.017 


.013 


.012 


25 


5 




.100 


.047 


.028 


.020 


.019 


25 


1 


.025 


.018 


.012 


.008 


.006 


•005 


27 


2 


.030 


.020 


.014 


.009 


.007 


.006 


28 


3 


.038 


.025 


.017 


.011 


.009 


.008 


29 


4 


.066 


.036 


.023 


.016 


.012 


.012 


30 
3i 


5 




.083 


.042 


.026 


.020 


.019 



42 



to Declinations for Latitude 40° N. 



,c 


1- a .2 














§°1 


1st 


July 


Aug. 


Sept. 


Oct. 


Nov. 


Dec. 
























i 


1 


0.005 


0.007 


O.OII 


0.016 


0.024 


0.032 


2 


2 


.006 


.008 


.012 


.018 


.027 


•037 


3 


3 


.008 


.010 


.015 


.023 


.035 


.050 


4 
5 


4 
5 


.012 
.019 


.015 
.024 


.020 
.036 


.032 
.068 


■057 


. 101 


6 


1 


.oo5 


.O'jS 


.012 


.018 


.026 


.033 


7 


2 


.007 


.009 


.013 


.019 


.029 




8 


3 


.009 


.011 


.016 


.024 


.038 


.051 


9 


4 


.012 


.015 


.022 


•035 


.063 


•'"7 


lO 


5 


.020 


.025 


.038 


.078 






1 1 


1 


.006 


.00S 


.013 


.019 


.027 




12 


2 


.007 


.009 


.014 


.021 


.031 




13 


3 


.009 


.011 


.017 


.026 


.040 


; 


'4 


4 


.012 


.016 


.024 


.038 


7 


.111 


15 


5 


.02 1 


.026 


•043 


.091 






[6 


1 


.oo5 


.009 


=013 


.020 


.029 


•034 


17 


2 


,007 


.010 


.015 


.022 


.033 




[8 


3 


.009 


.012 






.043 




19 


4 


.013 


•"'7 


.026 


.042 


•"7 s 


.113 


20 


5 


.021 


.1 128 




.114 






21 


1 


.006 


.010 


.014 


.021 


.030 




22 


2 


.007 


."i 1 


.016 


.024 






23 


3 


.009 


.013 


.019 


.030 


.045 




24 


4 


.013 






.046 






25 


5 


.021 


.030 


.051 


•Ml 






26 


1 




.010 


.015 








27 


2 




.01 1 




























•1 


•°'-1 


.019 












5 































III. — Refraction Corrections to be Applied to 

Altitudes. 

Pulcova Mean Refractions — Barom.=29".5, Att. Therm.=: 
50° F., Ext. Therm.=50° F. 



^J 


G 


^J 


a 


+j 


JH 




PJ 


£. v 


O 


a u 





3 <LI 


r*.2 


fl (U 





HJ Tj 




<U T3 


ti'g 


<U 'O 




(U ^ 




J-, 3 


a 


u 3 


cd 


«-< 3 


a3 u 


u d 


rf u 




v a 


<< 








rt .ti 


S45 


<< 


V 

04 




CD 


*« 




o 























9.67 


0.089 


15-67 


0.056 


22 50 


0.058 


38 


0.020 


10.00 


.087 


16.00 


■055 


23 00 


•037 


40 


0.019 


10.33 


.085 


16.33 


•°54 


23-50 


.036 


42 


0.018 


10.67 


.082 


16.67 


•053 


24.00 


•036 


44 


0.016 


11.00 


.080. 


17.00 


.052 


24.50 


•035 


46 


.015 


n-33 


.077 


-17-33 


.050 


25.00 


•034 


48 


.014 


11.67 


•075 


17.67 


.049 


26.00 


•032 


50 


• 013 


12.00 


•073 


18.00 


.048 


27.00 


.031 


52 


.013 


12.33 


071 


i8.33 


.047 


28.00 


.030 


54 


.012 


12 67 


.069 


18.67 


.046 


29.00 


.029 


56 


.011 


13.00 


.06S 


19.00 


•045 


30.00 


.028 1 


58 


.010 


13-33 


.066 


19-33 


•045 


31.00 


.027 1 


60 


.009 


13-67 


.064 


19.67 


.044 ! 


32.00 


.026 


65 


.008 


14.00 


.063 


20.00 


•043 


33-00 


•025 


70 


.006 


14-33 


.061 


20.50 


.042 


34.00 


024 


75 


.004 


14.67 


.060 


21.00 


.041 


35-00 


•023 


80 


.003 


15.00 


.058 


21.50 


.040 


36.00 


.022 


85 


.001 


15-33 


.057 


22.00 


•039 - 


37.00 


.021 


90 


00 



44 



11905 



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